Heriot-Watt University Research Gateway The influence of alcohol content variation in UK packaged beers on the uncertainty of calculations using the Widmark equation Citation for published version: Maskell, PD, Holmes, C, Huismann, M, Reid, S, Carr, M, Jones, BJ & Maskell, DL 2018, 'The influence of alcohol content variation in UK packaged beers on the uncertainty of calculations using the Widmark equation', Science and Justice, vol. 58, no. 4, pp. 271-275. https://doi.org/10.1016/j.scijus.2018.03.003 Digital Object Identifier (DOI): 10.1016/j.scijus.2018.03.003 Link: Link to publication record in Heriot-Watt Research Portal Document Version: Peer reviewed version Published In: Science and Justice General rights Copyright for the publications made accessible via Heriot-Watt Research Portal is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy Heriot-Watt University has made every reasonable effort to ensure that the content in Heriot-Watt Research Portal complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 15. Aug. 2021
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Heriot-Watt University Research Gateway
The influence of alcohol content variation in UK packaged beerson the uncertainty of calculations using the Widmark equation
Citation for published version:Maskell, PD, Holmes, C, Huismann, M, Reid, S, Carr, M, Jones, BJ & Maskell, DL 2018, 'The influence ofalcohol content variation in UK packaged beers on the uncertainty of calculations using the Widmarkequation', Science and Justice, vol. 58, no. 4, pp. 271-275. https://doi.org/10.1016/j.scijus.2018.03.003
Digital Object Identifier (DOI):10.1016/j.scijus.2018.03.003
Link:Link to publication record in Heriot-Watt Research Portal
Document Version:Peer reviewed version
Published In:Science and Justice
General rightsCopyright for the publications made accessible via Heriot-Watt Research Portal is retained by the author(s) and /or other copyright owners and it is a condition of accessing these publications that users recognise and abide bythe legal requirements associated with these rights.
Take down policyHeriot-Watt University has made every reasonable effort to ensure that the content in Heriot-Watt ResearchPortal complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact [email protected] providing details, and we will remove access to the work immediately andinvestigate your claim.
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[3] Office of National Statistics, Adult drinking habits in Great Britain - Office for National Statistics, 2017. https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/drugusealcoholandsmoking/bulletins/opinionsandlifestylesurveyadultdrinkinghabitsingreatbritain/2005to2016 (accessed November 22, 2017).
[4] B.K. Logan, G.A. Case, S. Distefano, Alcohol content of beer and malt beverages: forensic consideration., J. Forensic Sci. 44 (1999) 1292–1295.
[5] P.D. Maskell, R. Alex Speers, D.L. Maskell, Improving uncertainty in Widmark equation calculations: Alcohol volume, strength and density, Sci. Justice. (2017). doi:10.1016/j.scijus.2017.05.006.
[6] H. Government, THE FOOD LABELLING REGULATIONS 1996 :, (1996) 1–34. http://www.legislation.gov.uk/uksi/1996/1499/contents/made (accessed December 4, 2017).
[7] EU regulation 1169/2011, 2011. http://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX:32011R1169 (accessed October 30, 2017).
[8] Alcolyzer ME Measuring Module, (n.d.). https://www.anton-paar.com/?eID=documentsDownload&document=55783&L=38 (accessed October 30, 2017).
[9] J. Searle, Alcohol calculations and their uncertainty, Med. Sci. Law. 55 (2015) 58–64. doi:10.1177/0025802414524385.
[10] R.G. Gullberg, Estimating the uncertainty associated with Widmark’s equation as commonly applied in forensic toxicology, Forensic Sci. Int. 172 (2007) 33–39. doi:10.1016/j.forsciint.2006.11.010.
[13] P.E. Watson, I.D. Watson, R.D. Batt, Prediction of blood alcohol concentrations in human subjects. Updating the Widmark equation, J. Stud. Alcohol. 42 (1981).
[14] A.R.W. Forrest, The estimation of Widmark’s factor, J. Forensic Sci. Soc. 26 (1986).
[15] S. Seidl, U. Jensen, A. Alt, The calculation of blood ethanol concentrations in males and females, Int. J. Legal Med. 114 (2000). doi:10.1007/s004140000154.
Figure 1A: Histogram of the residuals of the 112 UK beers with a declared %ABV of
5.5% showing normal distribution.
Figure 1B: Histogram of the residuals of the 106 UK beers with a declared %ABV of
>5.5% showing normal distribution.
Figure 2: The %CV that should be utilised for uncertainty calculations when the
%ABV of the beer is known. The data is given for 1 (68 % CI), 2 (95 % CI) and 3
(99.7 % CI).
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
3.0 5.0 7.0 9.0 11.0 13.0
%C
V
Declared ABV (%v/v)
3s
2s
1s
Table 1: The %CV that should be utilised for uncertainty calculations when the %ABV of the beer is known. The data is given for 1
(68 % CI), 2(95 % CI) and 3 (99.7 % CI).
%ABV %CV
1
3.4 12.7 25.4 38.2
3.5 12.4 24.7 37.1
3.6 12.0 24.0 36.1
3.7 11.7 23.4 35.1
3.8 11.4 22.8 34.2
3.9 11.1 22.2 33.3
4.0 10.8 21.6 32.4
4.1 10.6 21.1 31.7
4.2 10.3 20.6 30.9
4.3 10.1 20.1 30.2
4.4 9.8 19.7 29.5
4.5 9.6 19.2 28.8
4.6 9.4 18.8 28.2
4.7 9.2 18.4 27.6
4.8 9.0 18.0 27.0
4.9 8.8 17.7 26.5
5.0 8.7 17.3 26.0
5.1 8.5 17.0 25.4
5.2 8.3 16.6 25.0
5.3 8.2 16.3 24.5
5.4 8.0 16.0 24.0
5.5 7.9 15.7 23.6
5.6 9.4 18.9 28.3
5.7 9.3 18.5 27.8
%ABV %CV
1 2 3
5.8 9.1 18.2 27.3
5.9 8.9 17.9 26.8
6.0 8.8 17.6 26.4
6.1 8.7 17.3 26.0
6.2 8.5 17.0 25.5
6.3 8.4 16.8 25.1
6.4 8.3 16.5 24.8
6.5 8.1 16.2 24.4
6.6 8.0 16.0 24.0
6.7 7.9 15.8 23.6
6.8 7.8 15.5 23.3
6.9 7.7 15.3 23.0
7.0 7.5 15.1 22.6
7.1 7.4 14.9 22.3
7.2 7.3 14.7 22.0
7.3 7.2 14.5 21.7
7.4 7.1 14.3 21.4
7.5 7.0 14.1 21.1
7.6 6.9 13.9 20.8
7.7 6.9 13.7 20.6
7.8 6.8 13.5 20.3
7.9 6.7 13.4 20.1
8.0 6.6 13.2 19.8
8.1 6.5 13.0 19.6
%ABV %CV
1 2 3
8.2 9.1 18.2 27.3
8.3 8.9 17.9 26.8
8.4 8.8 17.6 26.4
8.5 8.7 17.3 26.0
8.6 8.5 17.0 25.5
8.7 8.4 16.8 25.1
8.8 8.3 16.5 24.8
8.9 8.1 16.2 24.4
9.0 8.0 16.0 24.0
9.1 7.9 15.8 23.6
9.2 7.8 15.5 23.3
9.3 7.7 15.3 23.0
9.4 7.5 15.1 22.6
9.5 7.4 14.9 22.3
9.6 7.3 14.7 22.0
9.7 7.2 14.5 21.7
9.8 7.1 14.3 21.4
9.9 7.0 14.1 21.1
10.0 6.9 13.9 20.8
10.1 6.9 13.7 20.6
10.2 6.8 13.5 20.3
10.3 6.7 13.4 20.1
10.4 6.6 13.2 19.8
10.5 6.5 13.0 19.6
%ABV %CV
1 2 3
10.6 5.0 10.0 14.9
10.7 4.9 9.9 14.8
10.8 4.9 9.8 14.7
10.9 4.8 9.7 14.5
11.0 4.8 9.6 14.4
11.1 4.8 9.5 14.3
11.2 4.7 9.4 14.1
11.3 4.7 9.3 14.0
11.4 4.6 9.3 13.9
11.5 4.6 9.2 13.8
11.6 4.6 9.1 13.7
11.7 4.5 9.0 13.5
11.8 4.5 8.9 13.4
11.9 4.4 8.9 13.3
12.0 4.4 8.8 13.2
12.1 4.4 8.7 13.1
12.2 4.3 8.7 13.0
12.3 4.3 8.6 12.9
12.4 4.3 8.5 12.8
Table 2: Example variable values from a fictitious individual (and associated
uncertainties) used to estimate the blood alcohol concentration calculated with the
Widmark equation.
Variable Value Uncertainty (S.D.) % CV
Sex Male
Weight (kg) 70a 1.4 2.0a
Vd of ethanol (r; l/kg)
0.7a 0.064 9.2a
Volume of Drink
(v; ml) 568 (1 UK pint) 3.81b 0.67b
Alcohol Density
(d; g/ml) 0.78974b 5.9 x 10-4 b 0.06b
Strength of
Alcohol (z; % v/v) See Table 2c
Data from:
aGullberg [10]
bMaskell et al. [5]
cThis Study
Table 3: The proportion (as a percentage) that each variable of the Widmark equation contributes to estimating the uncertainty in
Co (the maximum theoretical BAC at the time the ethanol dose was administered) based on data from Tables 1 and 2.